Let $c_1, c_2, c_3, c_4$ be arbitrary constants. The order of the differential equation,corresponding to $y=c_1 e^x+c_2 e^{\log _{e} x}+c_3 \sin ^2 x-c_4\left(\cos ^2 x-1\right)$ is

The differential equation representing the family of curves $y^2=2 c(x+\sqrt{c})$,where $c$ is a positive parameter,is of

The differential equation satisfied by the function $y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \dots \infty}}}$ is

$y = e^x (A \cos x + B \sin x)$ is the solution of the differential equation

Let $a$ and $b$ be arbitrary constants and $C$ be a fixed constant. If $y = a e^{2x} + b x e^{2x} + C$ is the general solution of a differential equation,then the order of that differential equation is

The differential equation of the family of curves given by $y = a e^{2x} + b e^{5x}$,where $a$ and $b$ are parameters,is: